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In this work, we used a $32^3 \times 64 \times 32$, 2+1 flavor domain walllattice with Iwasaki+DSDR gauge action. The pion mass is 171 MeV and the kaonmass is 492 MeV. We implement the Glashow-Iliopoulos-Maiani (GIM) cancellationusing charm quark masses of 750 MeV and 592 MeV. This is an intermediatecalculation, in that we are using both a coarse lattice spacing (1/a = 1.37GeV)so we expect significant discretization error coming from charm quark mass andwe are also using unphysical kinematics for the pion. The main purpose of thiscalculation is to study the contribution from the two-pion intermediate statewhen the energy of a two-pion state is lower than that of the kaon, as well asthe corresponding finite volume correction to the $\Delta M_K$.

$K_L$ - $K_S$ mass difference computed with a 171 MeV pion mass